Find the greatest common factor of $75, 8,$ and $21$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of $75, 8,$ and $21$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}75 &=3\cdot5\cdot5\\\\\\\\ 8&=2\cdot2\cdot2\\\\\\\\ 21&=3\cdot7 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}75 &=3\cdot5\cdot5\cdot1\\\\\\\\ 8&=2\cdot2\cdot2\cdot1\\\\\\\\ 21&=3\cdot7\cdot1 \end{aligned}$ The greatest common factor of $75, 8,$ and $21$ is $1$.